In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.

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An Algorithm is a set of well-defined instructions designed to perform a specific set of tasks. Algorithms are used in Computer science to perform calculations, automatic reasoning, data processing, computations, and problem-solving.  We design an algorithm before we write the program code because the algorithm explains the logic of how the program will perform tasks. Design and Analysis of Algorithms (DAA) requires prior knowledge of basic programming and mathematics concepts and data structure concepts. Key topics related to DAA are: Introduction to Algorithm, Greedy algorithm, linked... Show more

In graphs, in which all vertices have an odd degree, the number of Hamiltonian cycles through any fixed edge is always even.